I am descendant from one of the other sons of Matthew Gallaway (Anderson Gallaway) so I don't have a lot of information on William Gallaway; other reseachers may be able to add more. I have seen a bible reference (in DAR files) confirming that William did remarry a Mary Green(e) after Mary Polly Regan; also there is an 1860 census entry for the second wife (Mary Gallaway) living with Sinia Gallaway Wilson, another daughter of William's who married a Wilson who is reported to be this Mary Greene (and not Mary Polly Regan Gallaway who died earlier). However, I should warn you that there are two William Gallaway's about this time; one was born in Darlington South Carolina and lived in Henry Co. Alabama. He is not the William Gallaway in Irene Dabney Gallway's book (one of Matthew Gallaway of Oglethorpe sons) but the two lines are often confused. The marriage of William Gallaway and Mary Greene does show up on one of those ancestry.com international marriage records, but they never have the source.